Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 36

Topic

Exponential Functions

Description

This math example illustrates the exponential function y = -1 * 10^-0.3x through both a table of values and a graph. The table presents x-y coordinates for x values from -2 to 2, demonstrating how the function's output changes as x increases. The accompanying graph provides a visual representation of this exponential decay function with a negative coefficient, highlighting its distinctive shape and behavior.

Exponential functions are fundamental in mathematics and have numerous real-world applications, such as modeling radioactive decay, population decline, and cooling processes. This collection of examples aids in teaching the topic by offering students diverse representations of exponential functions, enabling them to observe how different parameters influence the function's behavior, particularly when dealing with negative coefficients and exponents.

The importance of multiple worked-out examples in understanding exponential functions cannot be overstated. Each example in this set showcases a unique form of the exponential function, helping students identify patterns and comprehend how alterations in the base, coefficient, or exponent affect the function's graph and values. This variety of examples strengthens the concept and assists students in developing a more intuitive grasp of exponential behavior, especially in cases where the function exhibits decay rather than growth.

Teacher Script: "Let's examine the function y = -1 * 10^-0.3x. Notice how the y-values approach zero from the negative side as x increases. This is an interesting case of exponential decay with a negative coefficient. Compare this graph to our previous examples. How does the negative coefficient affect the orientation of the graph? Can you think of any real-world scenarios where we might see this type of exponential behavior?"

For a complete collection of math examples related to Exponential Functions click on this link: Math Examples: Exponential Functions Collection.